Nikolay Luzin, his students, adversaries, and defenders (notes on the history of Moscow mathematics, 1914-1936) Yury Neretin This is historical-mathematical and historical notes on Moscow mathematics 1914-1936. Nikolay Luzin was a central figure of that time. Pavel Alexandroff, Nina Bari, Alexandr Khinchin, Andrey Kolmogorov, Mikhail Lavrentiev, Lazar Lyusternik, Dmitry Menshov, Petr Novikov, Lev Sсhnirelman, Mikhail Suslin, and Pavel Urysohn were his students. We discuss the time of the great intellectual influence of Luzin (1915-1924), the time of decay of his school (1922-1930), a moment of his administrative power (1934-1936), and his fall in July 1936. But the thing which served as a source of Luzin’s inner drama turned out to be a source of his subsequent fame... Lazar Lyusternik [351] Il est temps que je m’arr ete: voici que je dis, ce que j’ai d´eclar´e, et avec raison, ˆetre inutile `adire. Henri Lebesgue, Preface to Luzin’s book, Leˇcons sur les ensembles analytiques et leurs applications, [288] Прошло сто лет и что ж осталось От сильных, гордых сих мужей, Столь полных волею страстей? Их поколенье миновалось Alexandr Pushkin ’Poltava’ There is a common idea that a life of Nikolay Luzin can be a topic of a Shakespeare drama. I am agree with this sentence but I am extremely far from an intention to realize this idea. The present text is an impassive historical-mathematical and historical investigation of Moscow mathematics of that time. On the other hand, this is more a story of its initiation and turning moments than a history of achievements. The notes contain English overview and the bibliography. The rest is written in arXiv:1710.10688v1 [math.HO] 29 Oct 2017 Russian. 1. Overview (English) 2. Was Luzin a victim of political persecutions? 3. Moscow mathematics and Luzin’s thesis 4. Luzin’s school: the creation and the chain reaction 5. Decay 6. The fate of set theory 7. Mathematics and philosophy 8. Students attack the teacher 9. Over the top 10. Young workers, left mathematicians, and red professors 11. The year, which disappeared from annals 1 2 12. From a dialectic republic to the MechMath Addendum. Few remarks on historical context 13. In the next inning 14. Historians and mathematicians 15. Playing with fire 16. After the shock-wave 17. Autumn of Luzin 18. Mathematics for non-mathematicians. 19. Afterword Bibliography 1. Overview 1.1. Overview. In 1914 Nikolay Luzin1 (9.12.1883–28.2.1950), a student of Dmitry Egorov, returned to Moscow after a 3-year trip to G¨ottingen and Paris. In 1915 he published the thesis ’Integral and trigonometric series’ and in a short time initiated a mathematical ’chain reaction’ (a sentence of Lavrentiev [279]) in Russia. Since the fall 1914 he gathered a group of young mathematicians for a work in theory of functions of a real variable and in descriptive set theory. The group included (in different periods of time) Luzin’s friends Vladimir Golubev, Ivan Privalov, Wac law Sierpi´nski, Vyacheslav Stepanov and Luzin’s students Pavel Ale- xandroff, Nina Bari, Alexandr Khinchin, Andrey Kolmogorov, Mikhail Lavrentiev, Lazar Lyusternik, Dmitry Menshov, Petr Novikov, Lev Sсhnirelman, Mikhail Suslin, Pavel Urysohn (also, Valery Glivenko, Lyudmila Keldysh, Alexey Lyapunov, and some others). During the fall 1920-1921 the group was called Lusitania, in the historical-mathematical literature this term usually is extended to the whole Luzin’s school 1915-1935. It is commonly recongnized that Luzin was the founder of the famous Moscow mathematical school of XX century and that Luzin and Lusitanians reached in 1920- 30s a great mathematical breakthrough. Quite soon the domain of investigations was extended to probability (Khinchin, Kolmogorov, Glivenko), topology (Alexand- roff, Urysohn, Pontryagin), number theory (Khinchin, Gelfond, Schnirelman), fluid dynamics (Lavrentiev, Golubev, M. Keldysh), variational and functional analysis (Lyusternik, Sсhnirelman, Kolmogorov, Raikov, Gelfand), differential equations (Stepanov, Petrovsky, Lyusternik), logics (Kolmogorov, Glivenko, Maltsev, Novikov), theory of function of a complex variable (Golubev, Luzin, Privalov, Lavrentiev). Menshov and Bari (and ocassionaly other Lusitanians) continued investigations in theory of functions of a real variable. Luzin himself with Novikov, L. Keldysh, Lyapunov continued works in descriptive set theory. Below we discuss this process, points of its branching, and the roles of Khinchin, Alexandroff, and Kolmogorov in this development. Starting late 1920s - early 1930s we observe the first students of Luzin’s students as Lev Pontryagin, Alexandr Gelfond, Anatoly Maltsev, Andrey Tikhonov, Alexandr Kurosh, Mstislav Keldysh (but a continuation of the story is beyond the scope of these notes). 1The complete name: Luzin Nikolay Nikolaevich, Russian: Лузин Николай Николаевич (in the old Russian orthography: Лузинъ Николай Николаевичъ), the French transliteration used in 1920-30s was Lusin Nicolas. 3 However, Luzin’s group decayed after a series of mathematical and personal conflicts in 1922-1930. Apparently, this process must be regarded as natural and positive, but conflicts between Luzin and his students were unusually hot. Let us say few words on another side of mathematical history of that time. Many Soviet scientists who became widely known as pure mathematicians parallelly worked in development of high technologies and in applications of mathematics for natural sciences. This was one of reasons of favor of mathematics in the Soviet society. For mathematicians parallel activities gave a possibility for a wider view to science. On a social level this gave to individuals certain degrees of independence of a pure mathematical establishment. Also, this provided many positions for ma- thematicians. Apparently, this process was initiated in the famous TsAGI (The central Aero- Hydrodynamical Institute), which became an initial point of a development of the aero-cosmic industry of the Soviet Union. The Institute was founded in December 1918 by the mathematician, plane designer and professor of mechanics Nikolay Zhu- kovsky, he was enlisted by the aerodynamicist and mathematician Sergey Chaplygin. In the mid-20s, the complex analyst Golubev joined to aerodynamical and aero- mechanical investigations. In 1933, Golubev became the first dean of the famous Mechanical and Mathematical department of the Moscow State University (below MechMath)... All biographies of Luzin published in 1950-1985 ’forgot’ his employment in TsAGI (1930-1936?). However, in this story, we will observe several well-known technologists and applied mathematicians who supported Luzin in heavy moments of his biography or mantained Luzin’s memory after his death2. The time of our story was complicated and stormy. A picture of the Soviet politics of 1920-30s contains a dense sequence of turning point, mistakes, crimes, corrections of mistakes, apologizes to suffered, new mistakes, new crimes, big catastrophes and big successes. If to draw this politics as a graph on the paper, we get a constructive proof of existence of a nowhere differentiable function. There were two post-revolutionary tsunamis. The first was called ’The Year of the great break’, it was happened in 1929-1930. The second tsunami came suddenly in May–July 1937 and finished in September–November 1938 (in Soviet Union, this was called The Year Thirty Seven). Some Lusitanians were political radicals, in particular they participated in the ’Great break’ and a local revolution in the Institute for Mechanics and Mathematics of the Moscow University (1929-1930)... At the first glance, at the end of 1920s fortune favoured Luzin. In 1927 he was elected as the corresponding member of the Soviet Academy of sciences, in 1929 as a real member. In 1928 Luzin was a vice-president of the International Mathematical Congress in Bolognia. In 1930 he published the monograph on descriptive set theory, Leˇcons sur les ensembles analytiques et leurs applications, which exposed researches of Luzin and his students Suslin, Alexandroff, Novikov, Lavrentiev, Keldysh, Seli- vanovsky. In the same 1930 there appeared the first version of Luzin’s textbook on Differential and Integral calculus for technical universities, later it it was revised 2In particular, Alexey Krylov, Sergey Chaplygin, Viktor Kulebakin, Alexandr Nekrasov, Leonid Sretensky. 4 many times (13 editions 1930-1942, the total size of editions was 270 000, and 7 editions of a completely new version 1946-1961, the total size 550 000). Apparently during 25 years Luzin’s books were the most popular mathematical text-book in Soviet engineering education... However, in mid 20s Luzin lost his significance as an intellectual leader of Moscow mathematics. It came the time of Khinchin, Kolmogorov, Alexandroff, Pontryagin (Alexandroff’s student), Gelfond (a student of Khinchin and Stepanov)... Luzin did not understand new mathematics, which was created in Moscow in 1920-30s. After a long trip abroad, Luzin returned to Moscow in 1930 and met various problems in 1930-1933: a crisis of his own scientific program, conflicts with former students, semi-fantastical situation in PhysMath Department of Moscow University3 in 1930-1931, heavy illnesses... However, after a reform of the Academy of Sciences 1933-34, his formal social weight started to grow... In March 1935 Luzin was confirmed as the President of the Mathematical group of the Soviet Academy Sciences. We must explain the sense of this assignment. First. The Academy of Science of the Soviet Union was a high collegium, which leaded a development of sciences and high technologies. The position of an academician was life-long. A social status (and salary) of an academician was very high during the whole Soviet time. At that time the number of members of the Academy of Sciences was small (in 01.01.1936 the number of real members was 98 persons, this covered all natural and humanitarian sciences and also high technologies, each person had a great weight). Second. In 1930-40s a person on an important position had a wide freedom of initiative and a big influence (but he was seriously responsible for results of his activity and his solutions).